Rotating Supermassive Black Holes (4) ...

The jets produced by rotating supermassive black holes often have velocities that approach the speed of light. For such relativistic jets, the special theory of relativity predicts that it is possible to observe apparent velocity on the celestial sphere that exceeds the speed of light. This is an optical illusion because the true velocity of the source emitting the light that we see is always less than c.
Superluminal Motion
Velocities that appear to exceed that of light in this manner are called superluminal velocities and the corresponding apparent motion is called superluminal motion (the adjective "superluminal" meaning literally "greater than light"). The essential ingredient that is required to produce the illusion of superluminal motion is a relativistic jet that is oriented very nearly in the observer's direction. The discussion of why this is so is somewhat technical since it involves the equations of special relativity (albeit very simple ones). We put the details in a box below for the interested student to pursue (see also this calculator, which solves the equations automatically). However, it isn't necessary to consult the details to appreciate the primary point: special relativity, which is built on the idea that no velocity can exceed that of light, predicts that under some conditions a velocity will give the illusion of exceeding c, even though the true velocity does not. If a relativistic jet pointed nearly toward us did not appear to give superluminal velocities, it would be an indication that the theory of special relativity was wrong!
A Superluminal Jet in the Blazar 3C 279
The top right figure illustrates apparent superluminal motion in the blazar/quasar 3C 279, which lies at redshift z = 0.534. The horizontal axis is position on the celestial sphere, with the scale given at the top in milli-arcseconds. At the bottom is a scale for the corresponding linear distance in light years, assuming the source to be moving at right angles to our line of sight. This scale was constructed from the angular measure using the distance to the blazar as derived from the observed redshift and the Hubble law (a redshift of z = 0.534 corresponds to a distance of almost 6 billion light years). The vertical axis is time of observation over about a 3 year period.

Notice the steady movement to the right of the outermost lump in the radio frequency jet of 3C 279 over the period of observation. Click the "Show Labels" button to see details of how this radio observation suggests that the outermost lump seen in the blazar jet is superluminal. From the elapsed time on the vertical axis and the apparent horizontal distance on the bottom horizontal axis, we may conclude that the source appears to move about 14 light years in a time of only about 2 years. This implies an apparent velocity 7 times the speed of light! As discussed in the box below, this is an illusion caused by the relativistic motion near our line of sight. The actual velocity of the source is a little less than c at all times. Thus, the observation of a superluminal jet is not a signal that Einstein was wrong, but rather (because he was right!) a signal that the jet is relativistic and is pointed almost directly at us.

Superluminal Motion in the M87 Optical Jet
Most superluminal motion has been observed with the high resolution of long baseline radio telescope arrays. However, superluminal motion has also been observed by the Hubble Space Telescope for the optical jet of the radio galaxy M87 in the Virgo Cluster. This animation illustrates the superluminal motion of the M87 optical jet.

Jets and Superluminal Velocities

The adjacent figure illustrates the observation of a source that moves at a velocity v < c while making an angle q with the observer's line of sight. According to special relativity, the transverse velocity relative to the speed of light c that the observer will observe for the source in its apparent motion on the sky is given by the formula at the top of the figure and denoted by vT/c.

You may verify easily by using this formula and your calculator that the apparent transverse velocity deduced from this formula can be greater than the speed of light c, even though the true velocity of the source v never exceeds c. In fact, if you investigate the formula you will find that if the angle q is small enough and the true velocity is close enough to c, the apparent transverse velocity can be made as much larger than the speed of light as you would like! There is, of course, no contradiction with the special theory of relativity. The apparent superluminal velocity is a kind of optical illusion wrought upon us by the effects of relativity. The true velocity is v, and it never exceeds the velocity of light. Note that is is necessary for v to be near c to observe superluminal motion. For non-relativistic velocities the apparent transverse velocity is never superluminal. Here is a Java calculator that may be used to investigate the dependence of superluminal motion on velocity and orientation angle of a jet.